Space of modular forms of level 380, weight 2, and Character 380.v

• Label: 380.2.v
• Level: $380$
• Weight: $2$
• Character orbit: 380.v
• Rep. character: $\chi_{380}(7,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $224$
• Newform subspaces: $3$
• Sturm bound: $120$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 380 = 2^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	380.v (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 380 \)
Character field:			\(\Q(\zeta_{12})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(120\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(380, [\chi])\).

	Total	New	Old
Modular forms	256	256	0
Cusp forms	224	224	0
Eisenstein series	32	32	0

Trace form

\( 224 q - 2 q^{2} - 4 q^{5} - 20 q^{8} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(380, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
380.2.v.a	$380$	$2$	380.v	380.v	$12$	$4$	$1$	$3.034$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(-4\)	\(6\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{12}]$	\(q+(-1-\zeta_{12}^{3})q^{2}+(2-\zeta_{12}-\zeta_{12}^{2}+\cdots)q^{3}+\cdots\)
380.2.v.b	$380$	$2$	380.v	380.v	$12$	$4$	$1$	$3.034$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(2\)	\(-6\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{12}]$	\(q+(1+\zeta_{12}-\zeta_{12}^{2})q^{2}+(-2+\zeta_{12}+\cdots)q^{3}+\cdots\)
380.2.v.c	$380$	$2$	380.v	380.v	$12$	$216$	$54$	$3.034$		None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{12}]$